Boolean grammars

A new generalization of context-free grammars is introduced: Boolean grammars allow the use of all set-theoretic operations as an integral part of the formalism of rules. Rigorous semantics for these grammars is defined by language equations in a way that allows to generalize some techniques from the theory of context-free grammars, including Chomsky normal form, Cocke-Kasami-Younger cubic-time recognition algorithm and some limited extension of the notion of a parse tree, which together allow to conjecture practical applicability of the new concept.

[1]  Oscar H. Ibarra,et al.  Characterizations and Computational Complexity of Systolic Trellis Automata , 1984, Theor. Comput. Sci..

[2]  Christian Choffrut,et al.  On real-time cellular automata and trellis automata , 2004, Acta Informatica.

[3]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[4]  Gheorghe Paun,et al.  Regulated Rewriting in Formal Language Theory , 1989 .

[5]  David J. Weir,et al.  The equivalence of four extensions of context-free grammars , 1994, Mathematical systems theory.

[6]  Werner Kuich,et al.  Semirings and Formal Power Series: Their Relevance to Formal Languages and Automata , 1997, Handbook of Formal Languages.

[7]  Alexander Okhotin.  Conjunctive Grammars and Systems of Language Equations , 2004, Programming and Computer Software.

[8]  Arto Salomaa,et al.  Systolic Trellis Automata: Stability, Decidability and Complexity , 1986, Inf. Control..

[9]  Gerald Gazdar,et al.  Applicability of Indexed Grammars to Natural Languages , 1988 .

[10]  Leslie G. Valiant,et al.  General Context-Free Recognition in Less than Cubic Time , 1975, J. Comput. Syst. Sci..

[11]  Alexander Okhotin,et al.  Conjunctive Grammars , 2001, J. Autom. Lang. Comb..

[12]  Daniel H. Younger,et al.  Recognition and Parsing of Context-Free Languages in Time n^3 , 1967, Inf. Control..

[13]  Alexander Okhotin,et al.  Whale calf, a parser generator for conjunctive grammars , 2002, CIAA'02.

[14]  Alexander Okhotin.  Decision Problems for Language Equations with Boolean Operations , 2003, ICALP.

[15]  Véronique Terrier,et al.  On Real Time One-Way Cellular Array , 1995, Theor. Comput. Sci..

[16]  William C. Rounds,et al.  LFP A Logic for Linguistic Descriptions and an Analysis of its Complexity , 1988, Comput. Linguistics.

[17]  Aravind K. Joshi,et al.  Tree Adjunct Grammars , 1975, J. Comput. Syst. Sci..

[18]  Alexander Okhotin,et al.  On the equivalence of linear conjunctive grammars and trellis automata , 2004, RAIRO Theor. Informatics Appl..

[19]  Alfred V. Aho,et al.  Indexed Grammars—An Extension of Context-Free Grammars , 1967, SWAT.

[20]  Ernst L. Leiss,et al.  Unrestricted Complementation in Language Equations Over a One-Letter Alphabet , 1994, Theor. Comput. Sci..

[21]  Alexander Okhotin,et al.  On the closure properties of linear conjunctive languages , 2003, Theor. Comput. Sci..

[22]  Walter L. Ruzzo.  On Uniform Circuit Complexity , 1981, J. Comput. Syst. Sci..

[23]  Wojciech Rytter.  On the recognition of context-free languages , 1984, Symposium on Computation Theory.

[24]  Arto Salomaa,et al.  Systolic trellis automatat , 1984 .

[25]  Seymour Ginsburg,et al.  Two Families of Languages Related to ALGOL , 1962, JACM.

[26]  Pierre Boullier,et al.  A Cubic Time Extension of Context-Free Grammars , 2000, Grammars.

[27]  Noam Chomsky,et al.  The Algebraic Theory of Context-Free Languages* , 1963 .

[28]  Richard P. Brent.  A PARALLEL ALGORITHM FOR CONTEXT-FREE PARSING , 2003 .

[29]  Ivan Hal Sudborough,et al.  A Note on Tape-Bounded Complexity Classes and Linear Context-Free languages , 1975, JACM.

[30]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.